A389774 - OEIS

A389774

Number of solid partitions of n with 7 parts.

86, 86, 299, 593, 1156, 1933, 3340, 5214, 8249, 12245, 18023, 25519, 35967, 49137, 66716, 88645, 116781, 151356, 194831, 247336, 312066, 389357, 482854, 593373, 725324, 879514, 1061412, 1272329, 1518315, 1801256, 2128390, 2501784, 2930041, 3415893, 3968792

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OFFSET

7,1

LINKS

Table of n, a(n) for n=7..41.

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-1,-1,0,1,1,2,0,0,0,-2,-1,-1,0,1,1,0,1,0,0,-1,-1,1).

FORMULA

G.f.: (3*q^24 + 20*q^23 + 3*q^22 + 64*q^21 + 109*q^20 + 171*q^19 + 168*q^18 + 268*q^17 + 323*q^16 + 460*q^15 + 326*q^14 + 337*q^13 + 270*q^12 + 264*q^11 + 208*q^10 + 127*q^9 + 86*q^7)/(Product_{k=1..7} (1 - q^k)).

PROG

(PARI)

A_q(N) = {Vec((3*q^24 + 20*q^23 + 3*q^22 + 64*q^21 + 109*q^20 + 171*q^19 + 168*q^18 + 268*q^17 + 323*q^16 + 460*q^15 + 326*q^14 + 337*q^13 + 270*q^12 + 264*q^11 + 208*q^10 + 127*q^9 + 86*q^7)/(prod(k=1, 7, 1-q^k) + O('q^(N+1))))}

CROSSREFS

Column k=7 of A380893.

Cf. A000219, A000293, A002836, A207542, A379277.

Sequence in context: A143759 A020665 A259084 * A058907 A045101 A020215

Adjacent sequences: A389771 A389772 A389773 * A389775 A389776 A389777

KEYWORD

nonn,easy

AUTHOR

John Tyler Rascoe, Oct 14 2025

STATUS

approved