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 A296775 Expansion of 1/Sum_{k>=0} A000326(k+1)*x^k. 1
 1, -5, 13, -27, 54, -108, 216, -432, 864, -1728, 3456, -6912, 13824, -27648, 55296, -110592, 221184, -442368, 884736, -1769472, 3538944, -7077888, 14155776, -28311552, 56623104, -113246208, 226492416, -452984832, 905969664, -1811939328, 3623878656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Israel, Table of n, a(n) for n = 0..3316 Wikipedia, Pentagonal number Index entries for linear recurrences with constant coefficients, signature (-2). FORMULA a(n) = -2*a(n-1) for n > 3. For n >= 3, a(n) = (-1)^n * 27 * 2^(n-3). - Vaclav Kotesovec, Dec 20 2017 G.f.: (1-x)^3/(1+2*x). - Robert Israel, Dec 20 2017 E.g.f.: (1/8)*(- 19 + 14*x - 2*x^2 + 27*exp(-2*x) ). - Alejandro J. Becerra Jr., Feb 16 2021 MAPLE 1, -5, 13, seq(-27*(-2)^i, i=0..50); # Robert Israel, Dec 20 2017 MATHEMATICA CoefficientList[Series[1/Sum[(k+1)*(3*k+2)*x^k/2, {k, 0, 30}], {x, 0, 30}], x] (* Vaclav Kotesovec, Dec 20 2017 *) Join[{1, -5, 13}, Table[(-1)^n * 27 * 2^(n-3), {n, 3, 30}]] (* Vaclav Kotesovec, Dec 20 2017 *) PROG (PARI) N=66; my(x='x+O('x^N)); Vec(1/sum(k=0, N, (k+1)*(3*k+2)/2*x^k)) (PARI) first(n) = Vec((1-x)^3/(1+2*x) + O(x^n)) \\ Iain Fox, Dec 20 2017 (Magma) [1, -5, 13] cat [-27*(-2)^(n-3): n in [3..50]]; // G. C. Greubel, Jan 04 2023 (SageMath) [1, -5, 13]+[-27*(-2)^(n-3) for n in range(3, 51)] # G. C. Greubel, Jan 04 2023 CROSSREFS Cf. A000326, A294372. Sequence in context: A079989 A062480 A027024 * A272045 A248860 A185039 Adjacent sequences: A296772 A296773 A296774 * A296776 A296777 A296778 KEYWORD sign AUTHOR Seiichi Manyama, Dec 20 2017 STATUS approved

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Last modified August 6 12:32 EDT 2024. Contains 374974 sequences. (Running on oeis4.)