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Search: id:A022571
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| A022571 |
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Expansion of Product (1+q^m)^6; m=1..inf. |
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+0
1
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| 1, 6, 21, 62, 162, 384, 855, 1806, 3648, 7110, 13434, 24702, 44361, 78006, 134592, 228302, 381300, 627840, 1020394, 1638528, 2601849, 4088780, 6363354, 9813504, 15005458, 22760262, 34261248, 51204222, 76005906, 112092438, 164296989
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", New York, Gordon and Breach Science Publishers, 1986-1992, p. 755, Eq. 6.2.2.2. MR0874986 (88f:00013)
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FORMULA
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Euler transform of period 2 sequence [6, 0, ...]. - Michael Somos, Jul 09 2005
Expansion of q^(-1/4)(eta(q^2)/eta(q))^6 in powers of q. - Michael Somos, Jul 09 2005
Expansion of q^(-1/4)(1/2)k^(1/2)/k' in powers of q. - Michael Somos Jul 09 2005
Given g.f. A(x), then B(x)=(x*A(x^4))^4 satisfies 0=f(B(x), B(x^2)) where f(u, v)=(4096uv+48u+1)v-u^2 . - Michael Somos Jul 09 2005
Given g.f. A(x), then B(x)=x*A(x^4) satisfies 0=f(B(x), B(x^3)) where f(u, v)=(u^2-v^2)^2 -uv(1+8uv)^2 . - Michael Somos Jul 09 2005
G.f.: Product_{k>0} (1+x^k)^6.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff( prod(k=1, n, 1+x^k, 1+x*O(x^n))^6, n)) /* Michael Somos Jul 09 2005 */
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CROSSREFS
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Sequence in context: A048476 A122678 A132130 this_sequence A117962 A105457 A134931
Adjacent sequences: A022568 A022569 A022570 this_sequence A022572 A022573 A022574
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KEYWORD
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nonn
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AUTHOR
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njas
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