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 A359659 a(n) = Sum_{k=0..n} k^(k * (n-k+1)). 3
 1, 2, 6, 45, 1051, 88602, 27121964, 37004504305, 198705527223757, 5595513387083114570, 686714367475480207331582, 468422339816915120237104999421, 1664212116512828935888786624225704855 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..51 FORMULA G.f.: Sum_{k>=0} (k * x)^k/(1 - k^k * x). G.f.: Sum_{k>=0} x^k/(1 - (k+1)^(k+1) * x). a(n) = A349893(n+1) - 1. PROG (PARI) a(n) = sum(k=0, n, k^(k*(n-k+1))); (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^k*x))) (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k+1)^(k+1)*x))) CROSSREFS Cf. A026898, A349893, A359658. Cf. A031971, A349836, A349883. Cf. A003101, A349882. Sequence in context: A255015 A347984 A229836 * A136557 A092662 A052811 Adjacent sequences: A359656 A359657 A359658 * A359660 A359661 A359662 KEYWORD nonn AUTHOR Seiichi Manyama, Jan 10 2023 STATUS approved

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Last modified December 11 02:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)