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 A022736 Expansion of 1/Product_{m>=1} (1 - m*q^m)^12. 2
 1, 12, 102, 688, 4029, 21156, 102246, 461448, 1967658, 7990996, 31110432, 116685288, 423366831, 1490904528, 5110173678, 17088259888, 55862240688, 178836472032, 561532752086, 1731639278904, 5250722230962 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 12, g(n) = n. - Seiichi Manyama, Aug 16 2023 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..5000 FORMULA a(0) = 1; a(n) = (12/n) * Sum_{k=1..n} A078308(k) * a(n-k). - Seiichi Manyama, Aug 16 2023 MATHEMATICA With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-12, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *) PROG (PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^-12)) \\ G. C. Greubel, Jul 25 2018 (Magma) n:=50; R:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^12:m in [1..n]])); // G. C. Greubel, Jul 25 2018 CROSSREFS Column k=12 of A297328. Cf. A078308. Sequence in context: A344366 A304504 A344279 * A261483 A082151 A125375 Adjacent sequences: A022733 A022734 A022735 * A022737 A022738 A022739 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 9 15:15 EDT 2024. Contains 375044 sequences. (Running on oeis4.)