A291975 a(n) = (4*n)! * [z^(4*n)] exp((cos(z) + cosh(z))/2 - 1).

1, 1, 36, 6271, 3086331, 3309362716, 6626013560301, 22360251390209461, 118214069460929849196, 926848347928901638652131, 10326354052861964007954596391, 157987763647812764532709527137476, 3227443522308474152275617569919520761

Offset

0,3

Comments

Row sums of A291452.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(4*n-1,4*k-1) * a(n-k). - Ilya Gutkovskiy, Jan 21 2020

Maple

A291975 := proc(n) exp((cos(z) + cosh(z))/2 - 1):
(4*n)!*coeff(series(%, z, 4*(n+1)), z, 4*n) end:
seq(A291975(n), n=0..12);

Mathematica

P[m_, n_] := P[m, n] = If[n == 0, 1, Sum[Binomial[m*n, m*k]*P[m, n - k]*x, {k, 1, n}]];
a[n_] := Module[{cl = CoefficientList[P[4, n], x]}, Sum[cl[[k + 1]]/k!, {k, 0, n}]];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jul 23 2019, after Peter Luschny in A291452 *)

Prog

(PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, n, a[1+n]=sum(k=1, n, binomial(4*n-1, 4*k-1) * a[1+n-k])); a} \\ Andrew Howroyd, Jan 21 2020

Crossrefs

Cf. A291452.

Sequence in context: A184135 A275050 A222336 * A307351 A268554 A326999

Adjacent sequences: A291972 A291973 A291974 * A291976 A291977 A291978

Keyword

nonn

Author

Peter Luschny, Sep 07 2017

Status

approved