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Search: id:A162433
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| 1, 10, 33, 76, 157, 264, 425, 626, 897, 1230, 1629, 2174, 2653, 3448, 4119, 4978, 6197, 7114, 8457, 9870, 11477, 13070, 15001, 17104, 19181, 21732, 24327, 26926, 30247, 33232, 36695, 40674, 44065, 48554, 52827, 57664, 62361, 67704, 73347, 78728
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^4 for n>=0 where S(x) = Sum_{n>=0} x^(n(n+1)/2).
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EXAMPLE
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The coefficients in the 4-th power of the series:
S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...
begin: [(1),(4,6),(8,13,12),(14,24,18,20),(32,24,31,40,30),...];
the sums of the grouped coefficients yield the initial terms of this sequence.
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PROGRAM
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(PARI) {a(n)=local(S=sum(m=0, n+1, x^(m*(m+1)/2))+O(x^((n+1)*(n+2)/2))); sum(m=n*(n+1)/2, n*(n+1)/2+n, polcoeff(S^4, m))}
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CROSSREFS
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Cf. A162430, A162431, A162432, A162434, A162435, A162427 (variant).
Sequence in context: A065149 A085490 A081437 this_sequence A003012 A020478 A094170
Adjacent sequences: A162430 A162431 A162432 this_sequence A162434 A162435 A162436
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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), Jul 03 2009
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