A094577 -id:A094577 - cp's OEIS frontend

A308537 a(n) = exp(-1) * Sum_{k>=0} (k + n - 1)!^n/(k!*(k - 1)!^n).

1, 1, 27, 104149, 192052025697, 401307330353526478576, 1891640643805444860923624673784723, 35720630453521390599442254755998585843785410691847, 4425335738067265257031641848982502946902371654704454173556393591653249

Offset: 0

Ilya Gutkovskiy, Jun 06 2019

nonn

Main diagonal of A182933.

Cf. A000110, A070227, A094577.

Table[Exp[-1] Sum[(k + n - 1)!^n/(k! (k - 1)!^n), {k, 0, Infinity}], {n, 0, 8}]

a(n) = A182933(n,n).

A308538 a(n) = exp(1) * Sum_{k>=0} (-1)^k(k(k + 1))^n/k!.

Original entry on oeis.org

1, -1, 3, -11, -47, 2111, -18589, -671803, 24578625, 328227551, -44122149981, -17436709707, 129678315723089, -1671362093527073, -621466693739336509, 16245508786340273349, 4705502566521408713473, -172007688705762528111809, -54084940569279187064459581

Offset: 0

Ilya Gutkovskiy, Jun 06 2019

sign

Cf. A000587, A020556, A090211, A094577.

Table[Exp[1] Sum[(-1)^k (k (k + 1))^n/k!, {k, 0, Infinity}], {n, 0, 18}]
Table[Sum[Binomial[n, k] BellB[2 n - k, -1], {k, 0, n}], {n, 0, 18}]

a(n) = Sum_{k=0..n} binomial(n,k)*A000587(2*n-k).

cp's OEIS Frontend

A308537 a(n) = exp(-1) * Sum_{k>=0} (k + n - 1)!^n/(k!*(k - 1)!^n).

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Programs

Mathematica

Formula

A308538 a(n) = exp(1) * Sum_{k>=0} (-1)^k(k(k + 1))^n/k!.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

cp's OEIS Frontend

A308537 a(n) = exp(-1) * Sum_{k>=0} (k + n - 1)!^n/(k!*(k - 1)!^n).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A308538 a(n) = exp(1) * Sum_{k>=0} (-1)^k*(k*(k + 1))^n/k!.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A308538 a(n) = exp(1) * Sum_{k>=0} (-1)^k(k(k + 1))^n/k!.