A381025 -id:A381025 - cp's OEIS frontend

A381023 Expansion of e.g.f. log(1-x)^4 * exp(x) / 24.

0, 0, 0, 0, 1, 15, 160, 1575, 15659, 163191, 1809905, 21474255, 272757166, 3703523824, 53631736795, 826097224680, 13497286183354, 233291225507890, 4254733292942982, 81680724157089634, 1646873959921840191, 34800264421134754997, 769198023696181428250, 17751664780107823096301

Offset: 0

Seiichi Manyama, Feb 12 2025

nonn

Column k=4 of A094816.

Cf. A381025.

nmax=23; CoefficientList[Series[Log[1-x]^4*Exp[x]/24, {x, 0, nmax}], x]Range[0, nmax]! (* Stefano Spezia, Feb 12 2025 *)

a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(k, 4, 1)));

a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k,4)|.

A381068 Expansion of e.g.f. -log(1-x)^3 * exp(-x) / (6 * (1-x)).

Original entry on oeis.org

0, 0, 0, 1, 6, 45, 355, 3094, 29596, 309602, 3523110, 43384451, 575296458, 8177866047, 124108103665, 2003376811864, 34282425365912, 620022977756068, 11818804007307308, 236852477229232869, 4978799197426813454, 109547060229435717041, 2518068124265761834239

Offset: 0

Seiichi Manyama, Feb 12 2025

nonn

Column k=4 of A269954 (with a different offset).

Cf. A381025, A381066.

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*abs(stirling(k+1, 4, 1)));

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * |Stirling1(k+1,4)|.

a(n) = A381066(n) + A381066(n+1).

cp's OEIS Frontend

A381023 Expansion of e.g.f. log(1-x)^4 * exp(x) / 24.

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