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Search: id:A084785
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| 1, 2, 5, 16, 66, 348, 2298, 18504, 176841, 1958746, 24661493, 347548376, 5415830272, 92410046544, 1712819553864, 34258146124320, 735267392077962, 16852848083339700, 410809882438699346, 10611174406149372736
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In the triangle (A084783), the diagonal (this sequence) is the self-convolution of the first column (A084784) and the row sums (A084786) gives the differences of the diagonal and the first column.
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FORMULA
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G.f. A(x) satisfies (1+x)^2 = A(x/(1+x))^2/A(x). - Michael Somos Feb 16 2006
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PROGRAM
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(PARI) A = matrix(25, 25); A[1, 1] = 1; rs = 1; print(1); for (n = 2, 25, sc = sum (i = 2, n - 1, A[i, 1]*A[n + 1 - i, 1]); A[n, 1] = rs - sc; rs = A[n, 1]; for (k = 2, n, A[n, k] = A[n, k - 1] + A[n - 1, k - 1]; rs += A[n, k]); print(A[n, n])); (Wasserman)
(PARI) {a(n)=local(A); if(n<0, 0, A=1; for(k=1, n, A=truncate(A+O(x^k))+x*O(x^k); A+=A-(subst(1/A, x, x/(1+x))*(1+x))^-2; ); polcoeff(A, n))} /* Michael Somos Feb 18 2006 */
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CROSSREFS
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Cf. A084783, A084784, A084786.
Sequence in context: A000522 A007469 A091139 this_sequence A124551 A005157 A019502
Adjacent sequences: A084782 A084783 A084784 this_sequence A084786 A084787 A084788
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 13 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jan 06 2005
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