A381307 E.g.f. A(x) satisfies A(x) = exp( x * cosh(x * A(x)^(1/2)) ).

1, 1, 1, 4, 25, 126, 841, 8303, 84561, 925480, 12285121, 181409427, 2840445169, 49113986936, 932675641353, 18883732449871, 408771283327969, 9499097097870720, 234457146543484225, 6115077874320445715, 168654204908597822241, 4902220448616467300248

Offset

0,4

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} (n/2-k/2+1)^(k-1) * A185951(n,k).

Prog

(PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (n/2-k/2+1)^(k-1)*a185951(n, k));

Crossrefs

Cf. A185951.

Sequence in context: A240479 A317949 A263440 * A240631 A123660 A304842

Adjacent sequences: A381304 A381305 A381306 * A381308 A381309 A381310

Keyword

nonn,new

Author

Seiichi Manyama, Feb 19 2025

Status

approved